Original Pref Length = 9600 Filtered Pref Length = 9478
Original Smallt Length = 9600 Filtered Smallt Length = 9453
Original Pilot Length = 13994 Filtered Pilot Length = 13994
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
| Duration | Linear Estimate | P-Value | Std Error |
|---|---|---|---|
| Circle | 3.196e-02 | 0.000e+00 | 1.022e-03 |
| Pilot | 3.830e-02 | 0.000e+00 | 8.766e-04 |
| Arc | 3.376e-02 | 0.000e+00 | 9.952e-04 |
| All | 3.518e-02 | 0.000e+00 | 5.549e-04 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 0.781±0.047 | 0.846±0.043 | 0.667±0.057 |
| 3.8 | 0.844±0.05 | 0.902±0.043 | 0.743±0.061 |
| 4.7 | 0.868±0.049 | 0.926±0.046 | 0.782±0.067 |
| 6.1 | 0.904±0.051 | 0.973±0.043 | 0.823±0.073 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 0.7804±0.0798 | 0.8456±0.0869 | 0.6674±0.1233 |
| 3.8 | 0.8432±0.0981 | 0.9020±0.1021 | 0.7428±0.1204 |
| 4.7 | 0.8669±0.1082 | 0.9268±0.0982 | 0.7814±0.1593 |
| 6.1 | 0.9039±0.1120 | 0.9733±0.1128 | 0.8228±0.1803 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 0.7804±0.0413 | 0.8456±0.0239 | 0.6674±0.0157 |
| 3.8 | 0.8432±0.0419 | 0.9020±0.0225 | 0.7428±0.0180 |
| 4.7 | 0.8669±0.0387 | 0.9268±0.0245 | 0.7814±0.0175 |
| 6.1 | 0.9039±0.0404 | 0.9733±0.0216 | 0.8228±0.0182 |
There is an overall effect of mass on movement duration (slope = 3.199e-02, p = 0.000e+00).
Experiment 2b movement duration is not different from 2a (p = 2.590e-01).
Experiment 2c movement duration is significantly lower than 2a (slope = -1.301e-01, p = 1.723e-03).
The interesting thing with these are the interaction effects.
Experiment 2b movement duration increases with mass more than experiment 2a (slope = 1.770e-03, p = 2.257e-01).
Experiment 2c movement duration increases with mass more than experiment 2a (slope = 6.323e-03, p = 2.284e-06).
Figure 1.1: Movement Duration by experiment.
| Duration | Linear Estimate | P-Value | Std Error |
|---|---|---|---|
| Circle | 4.152e-02 | 0.000e+00 | 1.304e-03 |
| Pilot | 5.797e-02 | 0.000e+00 | 1.313e-03 |
| Arc | 3.986e-02 | 0.000e+00 | 1.166e-03 |
| All | 4.803e-02 | 0.000e+00 | 7.529e-04 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 1±0.052 | 1±0.045 | 1±0.064 |
| 3.8 | 1.085±0.062 | 1.067±0.043 | 1.124±0.086 |
| 4.7 | 1.112±0.054 | 1.096±0.047 | 1.175±0.081 |
| 6.1 | 1.162±0.06 | 1.15±0.042 | 1.234±0.083 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 1.0000±0.0000 | 1.0000±0.0000 | 1.0000±0.0000 |
| 3.8 | 1.0849±0.1255 | 1.0666±0.0380 | 1.1238±0.1227 |
| 4.7 | 1.1115±0.0855 | 1.0963±0.0370 | 1.1749±0.1368 |
| 6.1 | 1.1614±0.1187 | 1.1503±0.0496 | 1.2338±0.1409 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 1.0000±0.0519 | 1.0000±0.0279 | 1.0000±0.0227 |
| 3.8 | 1.0849±0.0521 | 1.0666±0.0256 | 1.1238±0.0277 |
| 4.7 | 1.1115±0.0486 | 1.0963±0.0287 | 1.1749±0.0252 |
| 6.1 | 1.1614±0.0507 | 1.1503±0.0251 | 1.2338±0.0256 |
There is an overall effect of mass on movement duration (slope = 4.157e-02, p = 0.000e+00).
Experiment 2b movement duration is not different from 2a (p = 7.798e-01).
Experiment 2c movement duration is not different from 2a (p = 1.485e-01).
The interesting thing with these are the interaction effects.
Experiment 2b movement duration did NOT change with mass more than 2a. (p = 3.898e-01).
Experiment 2c movement duration increases with mass more than experiment 2a (slope = 1.641e-02, p = 0.000e+00).
(#fig:movedur_normbyexperiment)Movement Duration by experiment.
| Velocity | Linear Estimate | P-Value | Std Error |
|---|---|---|---|
| Circle | -1.300e-02 | 0.000e+00 | 2.736e-04 |
| Pilot | -1.990e-02 | 0.000e+00 | 3.156e-04 |
| Arc | -1.130e-02 | 0.000e+00 | 2.106e-04 |
| All | -1.544e-02 | 0.000e+00 | 1.692e-04 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 0.261±0.075 | 0.227±0.066 | 0.391±0.092 |
| 3.8 | 0.232±0.067 | 0.206±0.059 | 0.345±0.081 |
| 4.7 | 0.222±0.064 | 0.199±0.058 | 0.335±0.079 |
| 6.1 | 0.211±0.061 | 0.184±0.053 | 0.314±0.074 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 0.2610±0.0387 | 0.2274±0.0391 | 0.3913±0.1043 |
| 3.8 | 0.2322±0.0422 | 0.2059±0.0345 | 0.3451±0.0735 |
| 4.7 | 0.2228±0.0381 | 0.1991±0.0357 | 0.3350±0.0888 |
| 6.1 | 0.2113±0.0378 | 0.1838±0.0365 | 0.3136±0.0822 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 0.2610±0.0112 | 0.2274±0.0045 | 0.3913±0.0051 |
| 3.8 | 0.2322±0.0103 | 0.2059±0.0044 | 0.3451±0.0045 |
| 4.7 | 0.2228±0.0092 | 0.1991±0.0043 | 0.3350±0.0046 |
| 6.1 | 0.2113±0.0090 | 0.1838±0.0038 | 0.3136±0.0041 |
There is an overall effect of mass on peak velocity (slope = -1.300e-02, p = 0.000e+00).
Experiment 2b peak velocity is not different from 2a (p = 1.599e-01).
Experiment 2c peak velocity is significantly greater than 2a (slope = 1.453e-01, p = 2.233e-10).
The interesting thing with these are the interaction effects.
Experiment 2b peak velocity increases with mass more than experiment 2a (slope = 1.690e-03, p = 1.321e-04).
Experiment 2c peak velocity decreases with mass more than experiment 2a (slope = -6.910e-03, p = 0.000e+00).
Figure 1.2: Peak Velocity by experiment.
## boundary (singular) fit: see help('isSingular')
| Velocity | Linear Estimate | P-Value | Std Error |
|---|---|---|---|
| Circle | -4.881e-02 | 0.000e+00 | 1.027e-03 |
| Pilot | -5.037e-02 | 0.000e+00 | 7.768e-04 |
| Arc | -5.022e-02 | 0.000e+00 | 9.117e-04 |
| All | -4.987e-02 | 0.000e+00 | 5.215e-04 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 1±0.289 | 1±0.289 | 1±0.236 |
| 3.8 | 0.895±0.258 | 0.906±0.262 | 0.897±0.211 |
| 4.7 | 0.855±0.247 | 0.876±0.253 | 0.86±0.203 |
| 6.1 | 0.814±0.235 | 0.806±0.233 | 0.805±0.19 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 1.0000±0.0000 | 1.0000±0.0000 | 1.0000±0.0000 |
| 3.8 | 0.8950±0.1284 | 0.9063±0.0448 | 0.8967±0.0993 |
| 4.7 | 0.8553±0.1025 | 0.8756±0.0523 | 0.8603±0.0941 |
| 6.1 | 0.8145±0.1288 | 0.8061±0.0475 | 0.8049±0.0938 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 1.0000±0.0428 | 1.0000±0.0197 | 1.0000±0.0127 |
| 3.8 | 0.8950±0.0393 | 0.9063±0.0191 | 0.8967±0.0119 |
| 4.7 | 0.8553±0.0350 | 0.8756±0.0186 | 0.8603±0.0120 |
| 6.1 | 0.8145±0.0351 | 0.8061±0.0165 | 0.8049±0.0106 |
There is an overall effect of mass on peak velocity (slope = -4.876e-02, p = 0.000e+00).
Experiment 2b peak velocity is not different from 2a (p = 6.286e-01).
Experiment 2c peak velocity is not different from 2a (p = 7.392e-01).
The interesting thing with these are the interaction effects.
Experiment 2b peak velocity did NOT change with mass more than 2a. (p = 2.847e-01).
Experiment 2c peak velocity did NOT change with mass more than 2a. (p = 1.907e-01).
Figure 1.3: Peak Velocity by experiment.
| Reaction Time | Linear Estimate | P-Value | Std Error |
|---|---|---|---|
| Circle | 4.882e-03 | 0.000e+00 | 4.768e-04 |
| Pilot | 5.688e-03 | 0.000e+00 | 4.167e-04 |
| Arc | 6.182e-03 | 0.000e+00 | 4.260e-04 |
| All | 5.607e-03 | 0.000e+00 | 2.556e-04 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 0.184±0.015 | 0.208±0.018 | 0.201±0.014 |
| 3.8 | 0.194±0.024 | 0.217±0.018 | 0.214±0.02 |
| 4.7 | 0.198±0.019 | 0.22±0.017 | 0.219±0.016 |
| 6.1 | 0.203±0.02 | 0.232±0.018 | 0.223±0.02 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 0.1839±0.0231 | 0.2075±0.0214 | 0.2011±0.0223 |
| 3.8 | 0.1939±0.0281 | 0.2171±0.0180 | 0.2141±0.0357 |
| 4.7 | 0.1979±0.0302 | 0.2199±0.0143 | 0.2186±0.0327 |
| 6.1 | 0.2024±0.0315 | 0.2317±0.0227 | 0.2230±0.0359 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 0.1839±0.0140 | 0.2075±0.0084 | 0.2011±0.0054 |
| 3.8 | 0.1939±0.0231 | 0.2171±0.0084 | 0.2141±0.0076 |
| 4.7 | 0.1979±0.0176 | 0.2199±0.0085 | 0.2186±0.0062 |
| 6.1 | 0.2024±0.0179 | 0.2317±0.0085 | 0.2230±0.0078 |
There is an overall effect of mass on reaction_time (slope = 4.923e-03, p = 0.000e+00).
Experiment 2b reaction_time is not different from 2a (p = 9.261e-02).
Experiment 2c reaction_time is not different from 2a (p = 1.129e-01).
The interesting thing with these are the interaction effects.
Experiment 2b reaction_time did NOT change with mass more than 2a. (p = 6.315e-02).
Experiment 2c reaction_time did NOT change with mass more than 2a. (p = 2.144e-01).
Figure 1.4: Reaction Time by experiment.
## boundary (singular) fit: see help('isSingular')
| Reaction Time Norm | Linear Estimate | P-Value | Std Error |
|---|---|---|---|
| Circle | 2.584e-02 | 0.000e+00 | 2.428e-03 |
| Pilot | 2.774e-02 | 0.000e+00 | 1.935e-03 |
| Arc | 3.037e-02 | 0.000e+00 | 2.076e-03 |
| All | 2.800e-02 | 0.000e+00 | 1.235e-03 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 1±0.075 | 1±0.081 | 1±0.062 |
| 3.8 | 1.055±0.118 | 1.049±0.082 | 1.062±0.082 |
| 4.7 | 1.074±0.092 | 1.064±0.084 | 1.085±0.072 |
| 6.1 | 1.099±0.092 | 1.118±0.085 | 1.107±0.086 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 1.0000±0.0000 | 1.0000±0.0000 | 1.0000±0.0000 |
| 3.8 | 1.0542±0.0718 | 1.0488±0.0434 | 1.0615±0.0835 |
| 4.7 | 1.0738±0.0617 | 1.0640±0.0540 | 1.0847±0.0711 |
| 6.1 | 1.0984±0.0676 | 1.1184±0.0628 | 1.1068±0.0860 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 1.0000±0.0747 | 1.0000±0.0404 | 1.0000±0.0267 |
| 3.8 | 1.0542±0.1158 | 1.0488±0.0409 | 1.0615±0.0342 |
| 4.7 | 1.0738±0.0903 | 1.0640±0.0416 | 1.0847±0.0303 |
| 6.1 | 1.0984±0.0899 | 1.1184±0.0418 | 1.1068±0.0357 |
There is an overall effect of mass on reaction_time (slope = 2.607e-02, p = 0.000e+00).
Experiment 2b reaction_time is not different from 2a (p = 4.493e-01).
Experiment 2c reaction_time is not different from 2a (p = 9.755e-01).
The interesting thing with these are the interaction effects.
Experiment 2b reaction_time did NOT change with mass more than 2a. (p = 1.892e-01).
Experiment 2c reaction_time did NOT change with mass more than 2a. (p = 5.748e-01).
Figure 1.5: Reaction Time by experiment.
| Reaction Velocity | Linear Estimate | P-Value | Std Error |
|---|---|---|---|
| Circle | 1.028e-04 | 1.329e-01 | 6.838e-05 |
| Pilot | 2.559e-04 | 8.326e-05 | 6.504e-05 |
| Arc | 3.021e-04 | 1.109e-04 | 7.816e-05 |
| All | 2.213e-04 | 5.632e-08 | 4.076e-05 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | -5.649e-04±2.801e-03 | -2.308e-03±3.649e-03 | -1.598e-03±2.942e-03 |
| 3.8 | -6.079e-04±2.993e-03 | -1.914e-03±3.095e-03 | -1.265e-03±2.660e-03 |
| 4.7 | -1.601e-04±2.137e-03 | -1.422e-03±2.856e-03 | -8.780e-04±2.124e-03 |
| 6.1 | -2.491e-04±2.646e-03 | -1.242e-03±2.679e-03 | -6.478e-04±2.186e-03 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | -0.0006±0.0011 | -0.0023±0.0022 | -0.0016±0.0017 |
| 3.8 | -0.0006±0.0016 | -0.0019±0.0018 | -0.0013±0.0012 |
| 4.7 | -0.0002±0.0012 | -0.0014±0.0014 | -0.0009±0.0014 |
| 6.1 | -0.0003±0.0020 | -0.0012±0.0010 | -0.0007±0.0014 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | -0.0006±0.0028 | -0.0023±0.0018 | -0.0016±0.0013 |
| 3.8 | -0.0006±0.0030 | -0.0019±0.0015 | -0.0013±0.0011 |
| 4.7 | -0.0002±0.0021 | -0.0014±0.0014 | -0.0009±0.0009 |
| 6.1 | -0.0003±0.0026 | -0.0012±0.0013 | -0.0007±0.0009 |
There is NOT an overall effect of mass on reaction_ (p = 2.407e-01).
Experiment 2b reaction_ is significantly lower than 2a (slope = -2.237e-03, p = 1.427e-03).
Experiment 2c reaction_ is significantly lower than 2a (slope = -1.437e-03, p = 2.498e-02).
The interesting thing with these are the interaction effects.
Experiment 2b reaction_ increases with mass more than experiment 2a (slope = 2.144e-04, p = 4.583e-02).
Experiment 2c reaction_ did NOT change with mass more than 2a. (p = 8.859e-02).
Figure 1.6: Reaction by experiment.
These next plots are made to try and show the effect of reaction time algorithms on reaction. Figure 1.7 shows the reaction time by experiment and algorithm. Figure @ref(fig:reactiontanvelalgoplot1} shows the velocity at reaction time by the experiments and algorithms. This plot shows that my algorithm is detecting movement onset at very very low movement speeds, whereas other methods detect it at MUCH higher movement speeds.
Figure 1.7: Reaction Time Algorithm method.
Figure 1.8: Reaction Velocity Algorithm method.
| Reaction Time % | Linear Estimate | P-Value | Std Error |
|---|---|---|---|
| Circle | -3.695e-03 | 7.220e-11 | 5.670e-04 |
| Pilot | -8.975e-03 | 0.000e+00 | 6.127e-04 |
| Arc | -2.735e-03 | 1.738e-07 | 5.234e-04 |
| All | -5.642e-03 | 0.000e+00 | 3.427e-04 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 0.243±0.022 | 0.254±0.024 | 0.322±0.028 |
| 3.8 | 0.236±0.026 | 0.248±0.022 | 0.302±0.027 |
| 4.7 | 0.233±0.023 | 0.245±0.021 | 0.296±0.026 |
| 6.1 | 0.228±0.02 | 0.244±0.02 | 0.286±0.024 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 0.2425±0.0228 | 0.2539±0.0322 | 0.3210±0.0600 |
| 3.8 | 0.2355±0.0253 | 0.2480±0.0299 | 0.3018±0.0473 |
| 4.7 | 0.2334±0.0254 | 0.2449±0.0269 | 0.2957±0.0550 |
| 6.1 | 0.2279±0.0195 | 0.2440±0.0238 | 0.2854±0.0488 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 0.2425±0.0207 | 0.2539±0.0111 | 0.3210±0.0105 |
| 3.8 | 0.2355±0.0249 | 0.2480±0.0102 | 0.3018±0.0106 |
| 4.7 | 0.2334±0.0218 | 0.2449±0.0100 | 0.2957±0.0098 |
| 6.1 | 0.2279±0.0194 | 0.2440±0.0096 | 0.2854±0.0090 |
There is an overall effect of mass on reaction_time (slope = -3.637e-03, p = 1.106e-08).
Experiment 2b reaction_time is not different from 2a (p = 5.625e-01).
Experiment 2c reaction_time is significantly greater than 2a (slope = 9.070e-02, p = 6.258e-10).
The interesting thing with these are the interaction effects.
Experiment 2b reaction_time increases with mass more than experiment 2a (slope = 8.950e-04, p = 3.211e-01).
Experiment 2c reaction_time decreases with mass more than experiment 2a (slope = -5.340e-03, p = 1.000e-10).
Figure 1.9: Reaction Time by experiment.
| Miss Distance | Linear Estimate | P-Value | Std Error |
|---|---|---|---|
| Circle | -7.373e-05 | 4.278e-03 | 2.581e-05 |
| Pilot | 1.002e-03 | 0.000e+00 | 9.763e-05 |
| Arc | -1.478e-04 | 5.039e-06 | 3.240e-05 |
| All | 3.547e-04 | 1.998e-15 | 4.469e-05 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 0.661±0.104 | 0.914±0.15 | 12.932±0.497 |
| 3.8 | 0.647±0.109 | 0.851±0.137 | 13.181±0.483 |
| 4.7 | 0.638±0.109 | 0.877±0.144 | 13.365±0.513 |
| 6.1 | 0.633±0.107 | 0.844±0.135 | 13.269±0.493 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 0.0066±0.0014 | 0.0092±0.0023 | 0.1292±0.0142 |
| 3.8 | 0.0065±0.0014 | 0.0085±0.0018 | 0.1317±0.0133 |
| 4.7 | 0.0064±0.0016 | 0.0088±0.0020 | 0.1336±0.0143 |
| 6.1 | 0.0063±0.0014 | 0.0084±0.0018 | 0.1326±0.0137 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 0.6605±0.0968 | 0.9153±0.0680 | 12.9228±0.1605 |
| 3.8 | 0.6466±0.1016 | 0.8513±0.0643 | 13.1727±0.1608 |
| 4.7 | 0.6369±0.1003 | 0.8777±0.0667 | 13.3561±0.1694 |
| 6.1 | 0.6335±0.1002 | 0.8441±0.0628 | 13.2610±0.1627 |
There is NOT an overall effect of mass on endpoint error (p = 2.960e-01).
Experiment 2b endpoint error is not different from 2a (p = 4.829e-01).
Experiment 2c endpoint error is significantly greater than 2a (slope = 1.206e-01, p = 0.000e+00).
The interesting thing with these are the interaction effects.
Experiment 2b endpoint error decreases with mass more than experiment 2a (slope = -6.361e-05, p = 5.881e-01).
Experiment 2c endpoint error increases with mass more than experiment 2a (slope = 1.085e-03, p = 0.000e+00).
Figure 1.10: Miss Distance (cm) by experiment.
(#fig:missdist_normbyexperiment)Movement Duration by experiment.
| Miss Distance Norm | Linear Estimate | P-Value | Std Error |
|---|---|---|---|
| Circle | -1.154e-02 | 3.186e-03 | 3.913e-03 |
| Pilot | 8.268e-03 | 0.000e+00 | 7.304e-04 |
| Arc | -1.242e-02 | 5.118e-04 | 3.575e-03 |
| All | -3.381e-03 | 3.159e-02 | 1.573e-03 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 100±14.64 | 100±14.613 | 100±2.748 |
| 3.8 | 98.249±15.688 | 94.892±14.548 | 102.194±3.143 |
| 4.7 | 96.158±15.267 | 96.785±14.624 | 103.581±3.337 |
| 6.1 | 95.886±15.303 | 94.044±14.374 | 102.817±3.158 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 1.0000±0.0000 | 1.0000±0.0000 | 1.0000±0.0000 |
| 3.8 | 0.9828±0.1035 | 0.9493±0.1307 | 1.0217±0.0599 |
| 4.7 | 0.9615±0.0816 | 0.9683±0.0963 | 1.0357±0.0671 |
| 6.1 | 0.9594±0.0875 | 0.9410±0.1344 | 1.0282±0.0586 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 100.0000±14.6784 | 100.0000±7.3208 | 100.0000±1.1792 |
| 3.8 | 98.2825±15.4628 | 94.9252±7.0642 | 102.1686±1.2122 |
| 4.7 | 96.1539±15.1376 | 96.8256±7.2042 | 103.5713±1.2697 |
| 6.1 | 95.9392±15.1536 | 94.0987±6.9610 | 102.8244±1.2254 |
There is an overall effect of mass on endpoint error (slope = -1.131e-02, p = 1.089e-04).
Experiment 2b endpoint error is not different from 2a (p = 7.209e-01).
Experiment 2c endpoint error is not different from 2a (p = 1.568e-01).
The interesting thing with these are the interaction effects.
Experiment 2b endpoint error did NOT change with mass more than 2a. (p = 7.684e-01).
Experiment 2c endpoint error increases with mass more than experiment 2a (slope = 1.954e-02, p = 2.545e-07).
Figure 1.11: Miss Distance Norm (cm) by experiment.
| Miss Distance | Linear Estimate | P-Value | Std Error |
|---|---|---|---|
| Circle | 2.200e-01 | 6.441e-01 | 4.762e-01 |
| Pilot | 2.013e+00 | 4.722e-01 | 2.799e+00 |
| Arc | -2.758e-01 | 6.754e-01 | 6.588e-01 |
| All | 8.466e-01 | 4.873e-01 | 1.219e+00 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 3.326±0.436 | 20.073±4.746 | 86.234±15.391 |
| 3.8 | 2.908±0.382 | 15.926±3.185 | 95.583±25.458 |
| 4.7 | 6.011±2.838 | 20.423±4.499 | 91.745±18.894 |
| 6.1 | 3.42±0.408 | 17.868±3.325 | 95.2±18.735 |
There is NOT an overall effect of mass on miss angle variance (p = 9.235e-01).
Experiment 2b miss angle variance is not different from 2a (p = 5.163e-01).
Experiment 2c miss angle variance is significantly greater than 2a (slope = 8.037e+01, p = 6.922e-04).
The interesting thing with these are the interaction effects.
Experiment 2b miss angle variance decreases with mass more than experiment 2a (slope = -4.958e-01, p = 8.784e-01).
Experiment 2c miss angle variance did NOT change with mass more than 2a. (p = 5.446e-01).
Figure 1.12: Miss Angle Variance (deg^2) by experiment.
| Miss Distance | Linear Estimate | P-Value | Std Error |
|---|---|---|---|
| Circle | -4.352e-03 | 3.409e-01 | 4.570e-03 |
| Pilot | 3.246e-01 | 1.838e-03 | 1.042e-01 |
| Arc | -9.412e-03 | 2.239e-03 | 3.079e-03 |
| All | 1.352e-01 | 3.875e-03 | 4.680e-02 |
| Effective Mass (kg) | 2a | 2b | 2c |
|---|---|---|---|
| 2.5 | 0.2808±0.0167 | 0.2528±0.0173 | 1.518±0.5973 |
| 3.8 | 0.2602±0.0139 | 0.2314±0.0154 | 2.015±0.5981 |
| 4.7 | 0.267±0.0241 | 0.226±0.0202 | 2.4844±0.4862 |
| 6.1 | 0.2618±0.0223 | 0.2165±0.013 | 2.7002±0.4948 |
There is NOT an overall effect of mass on miss radial variance (p = 9.586e-01).
Experiment 2b miss radial variance is not different from 2a (p = 9.859e-01).
Experiment 2c miss radial variance is not different from 2a (p = 5.075e-01).
The interesting thing with these are the interaction effects.
Experiment 2b miss radial variance did NOT change with mass more than 2a. (p = 9.660e-01).
Experiment 2c miss radial variance increases with mass more than experiment 2a (slope = 3.289e-01, p = 2.367e-03).
Figure 1.13: Miss Radial Variance by experiment.
Figure 1.14: Miss Rad Variance (cm^2) broken by experiment.
## Scale for y is already present.
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Figure 1.15: Velocity trajectories by experiment.
Figure 1.16: Velocity trajectories by experiment.
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Figure 1.17: Velocity trajectories by experiment.
Figure 1.18: Velocity trajectories by experiment.
Even though the preferred looks the same, just turns out the two velocity profiles are REALLY REALLY similar, but slightly different. This is shown in the following plot, that is zoomed into the peak velocities.
We filtered the metabolic data and removed any trial where the miss distance at endpoint was greater than 10 cm, the movement duration was less than 0.2 seconds, or the reaction time was greater than 0.50 s.This removed 13 out of 15975 original data points.
## Analysis of Variance Table
##
## Response: movedur
## Df Sum Sq Mean Sq F value Pr(>F)
## speed 1 1099.40 1099.40 1.0453e+05 <2e-16 ***
## eff_mass2 1 0.01 0.01 6.3430e-01 0.4258
## Residuals 15959 167.85 0.01
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Simultaneous Tests for General Linear Hypotheses
##
## Fit: lmer(formula = movedur ~ speed + eff_mass2 + (1 | subj), data = metdata_factor)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) == 0 2.498e-01 8.172e-03 30.571 <2e-16 ***
## speed == 0 1.544e-01 4.760e-04 324.257 <2e-16 ***
## eff_mass2 == 0 5.641e-06 2.371e-04 0.024 0.981
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
##
## Simultaneous Tests for General Linear Hypotheses
##
## Fit: lmer(formula = log(metpowergross) ~ log(movedur) + effmass2 +
## (1 | subject), data = mpdata)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) == 0 4.561517 0.066021 69.092 < 2e-16 ***
## log(movedur) == 0 -0.766794 0.037690 -20.345 < 2e-16 ***
## effmass2 == 0 0.017373 0.003369 5.156 2.52e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
## NULL
| Speed = 1 | Speed = 2 | Speed = 3 | Speed = 4 | Speed = 5 | Speed = 6 | Speed = 7 | |
|---|---|---|---|---|---|---|---|
| 2.73 kg | 171.9775 ± 18.515 | 131.625 ± 14.3282 | 110.1838 ± 5.8343 | 98.8513 ± 7.9976 | 105.3988 ± 8.8935 | 99.835 ± 7.0959 | NaN ± NA |
| 4.83 kg | 187.4712 ± 17.3187 | 153.6538 ± 13.0638 | 126.0213 ± 8.2191 | 104.4825 ± 6.9769 | 97.5825 ± 7.3818 | 97.2367 ± 5.4622 | NaN ± NA |
| 7.13 kg | NaN ± NA | 185.5288 ± 19.5249 | 140.2988 ± 11.6277 | 112.705 ± 6.8381 | 109.9457 ± 8.6896 | 98.7512 ± 7.5674 | 93.9238 ± 7.265 |
| 11.69 kg | NaN ± NA | 222.0612 ± 24.3934 | 155.0838 ± 13.5348 | 117.4025 ± 10.6555 | 110.285 ± 10.4558 | 96.8338 ± 5.2816 | 92.7812 ± 6.6335 |
Figure 2.1: Gross metabolic power.
Parameter estimates are showing as mean +- standard error. The columns are for without the subject mass coefficient, and with a mass coefficient on the effort model. Subj Mass Coef is the subject mass exponent.
The no_mass_coef model is as follows: \[ \dot{e} = a+\frac{bm^c}{T_m^d} \]
The Subject mass model times a1 is as follows: \[ \dot{e} = a*Body Mass^{f}+\frac{bm^c}{T_m^d} \]
The effective mass model times a1 is as follows: \[ \dot{e} = a*Effective\, Mass^{f}+\frac{bm^c}{T_m^d} \]
| a only | a*subject mass | a*effective mass | |
|---|---|---|---|
| a | 98.2501±3.0512 | 22.0844±13.6907 | 101.4027±7.5926 |
| b | 0.864±0.4319 | 0.8593±0.4234 | 0.8375±0.4215 |
| c | 0.8308±0.0998 | 0.8247±0.0981 | 0.8548±0.1107 |
| d | 5.8254±0.603 | 5.8562±0.5956 | 5.8035±0.6061 |
| f | null | 0.2983±0.1232 | -0.0187±0.0411 |
| SSE | 120872.749595644 | 116826.723834405 | 120743.074844557 |
| AIC | 1750.832 | 1746.4653 | 1752.6313 |
| BIC | 1766.9875 | 1765.852 | 1772.0179 |
##
## Simultaneous Tests for General Linear Hypotheses
##
## Fit: lmer(formula = log(metpowernet) ~ log(movedur) + effmass2 + (1 |
## subject), data = mpdata)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) == 0 2.85218 0.23454 12.161 < 2e-16 ***
## log(movedur) == 0 -2.37941 0.16610 -14.326 < 2e-16 ***
## effmass2 == 0 0.04912 0.01485 3.308 0.00094 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
| Speed = 1 | Speed = 2 | Speed = 3 | Speed = 4 | Speed = 5 | Speed = 6 | Speed = 7 | |
|---|---|---|---|---|---|---|---|
| 2.73 kg | 99.075 ± 17.3755 | 57.7875 ± 15.0154 | 36.3125 ± 5.9248 | 24.9875 ± 6.1351 | 31.5325 ± 8.1858 | 27.9333 ± 5.6508 | NaN ± NA |
| 4.83 kg | 113.7375 ± 18.2929 | 79.9875 ± 13.8077 | 52.3875 ± 8.9795 | 30.8212 ± 5.8168 | 23.9213 ± 7.2462 | 24.4667 ± 4.0208 | NaN ± NA |
| 7.13 kg | NaN ± NA | 111.7875 ± 19.9953 | 65.4 ± 11.9993 | 37.8638 ± 7.2397 | 37.7043 ± 7.8668 | 23.8963 ± 6.5959 | 19.0538 ± 6.8651 |
| 11.69 kg | NaN ± NA | 150.475 ± 22.0585 | 83.35 ± 13.048 | 45.6812 ± 10.4043 | 38.5625 ± 9.4318 | 25.0825 ± 5.0728 | 21.0525 ± 5.3099 |
Figure 2.2: Net metabolic power.
Parameter estimates are showing as mean +- standard error. The columns are for without the subject mass coefficient, and with a mass coefficient on the effort model. Subj Mass Coef is the subject mass exponent.
The no_mass_coef model is as follows: \[ \dot{e} = a+\frac{bm^c}{T_m^d} \]
The Subject mass model times a1 is as follows: \[ \dot{e} = a*Body Mass^{f}+\frac{bm^c}{T_m^d} \]
The effective mass model times a1 is as follows: \[ \dot{e} = a*Effective\, Mass^{f}+\frac{bm^c}{T_m^d} \]
| a only | a*subject mass | a*effective mass | |
|---|---|---|---|
| a | 24.7227±2.9124 | 0.1006±0.2368 | 24.0136±7.0227 |
| b | 1.0308±0.467 | 1.0007±0.4474 | 1.031±0.4707 |
| c | 0.7964±0.0904 | 0.7942±0.089 | 0.7962±0.1007 |
| d | 5.6574±0.5473 | 5.7151±0.5413 | 5.6575±0.5519 |
| f | null | 1.0939±0.4615 | 5e-04±0.1585 |
| SSE | 105365.400000357 | 101455.132835216 | 105365.395173997 |
| AIC | 1725.1562 | 1720.0843 | 1727.1561 |
| BIC | 1741.3117 | 1739.4709 | 1746.5428 |
| Speed = 1 | Speed = 2 | Speed = 3 | Speed = 4 | Speed = 5 | Speed = 6 | Speed = 7 | |
|---|---|---|---|---|---|---|---|
| 2.73 kg | 93.3222 ± 8.9748 | 80.1472 ± 7.2013 | 82.5764 ± 3.4054 | 94.0607 ± 9.0851 | 117.4043 ± 9.7673 | 125.4443 ± 10.8215 | NaN ± NA |
| 4.83 kg | 104.3653 ± 7.7764 | 95.0103 ± 5.6431 | 96.0467 ± 6.7137 | 97.5592 ± 7.0411 | 109.7052 ± 8.5622 | 123.3466 ± 10.6279 | NaN ± NA |
| 7.13 kg | NaN ± NA | 108.7596 ± 10.3474 | 95.2653 ± 7.1374 | 96.7068 ± 6.2899 | 113.0375 ± 8.3502 | 120.2383 ± 9.9578 | 130.8822 ± 10.7193 |
| 11.69 kg | NaN ± NA | 134.6313 ± 12.7635 | 106.7865 ± 8.1232 | 101.0186 ± 8.5022 | 112.9603 ± 9.2217 | 118.1752 ± 7.0501 | 128.0428 ± 9.1786 |
Figure 2.3: Gross metabolic cost.
The linear slope of the metabolic minimum is 0.0170765.
The optimal movement durations using the preferred masses are shown below along with the average movement durations.
| Effective Mass (kg) | Minimum Cost Duration (s) | Minimum Cost (J) | |
|---|---|---|---|
| a1 | 2.44 | 0.6627202 | 78.60625 |
| a1 | 4.83 | 0.7277517 | 86.31782 |
| a1 | 7.13 | 0.7693100 | 91.24823 |
| a1 | 11.69 | 0.8254945 | 97.91511 |
| Effective Mass (kg) | Minimum Cost (J) | Minimum Cost Duration (s) | Preferred Duraiton (s) | |
|---|---|---|---|---|
| a1 | 2.506 | 78.60625 | 0.6627202 | 0.7806626 |
| a1 | 3.959 | 83.90409 | 0.7073980 | 0.8441430 |
| a1 | 4.894 | 86.48003 | 0.7291192 | 0.8676516 |
| a1 | 5.282 | 89.61512 | 0.7555548 | 0.9044893 |
| Speed = 1 | Speed = 2 | Speed = 3 | Speed = 4 | Speed = 5 | Speed = 6 | Speed = 7 | |
|---|---|---|---|---|---|---|---|
| 2.73 kg | 53.1932 ± 8.5657 | 34.0816 ± 8.4267 | 26.267 ± 3.4663 | 23.2311 ± 5.6268 | 33.9323 ± 8.6921 | 35.0672 ± 7.0593 | NaN ± NA |
| 4.83 kg | 62.5789 ± 9.018 | 48.3557 ± 6.9453 | 39.0854 ± 6.5272 | 27.9088 ± 5.0761 | 25.9021 ± 7.7596 | 31.196 ± 5.3426 | NaN ± NA |
| 7.13 kg | NaN ± NA | 65.0537 ± 11.2371 | 44.2351 ± 7.8498 | 32.5745 ± 6.4326 | 38.6832 ± 7.8991 | 29.137 ± 8.1055 | 26.4202 ± 9.651 |
| 11.69 kg | NaN ± NA | 90.9807 ± 11.7824 | 57.1 ± 8.418 | 39.0674 ± 8.6669 | 38.9813 ± 8.9591 | 30.4859 ± 6.2224 | 28.82 ± 7.2275 |
Figure 2.4: Net metabolic cost.
The optimal movement durations using the preferred masses are shown below along with the average movement durations.
| Effective Mass (kg) | Minimum Cost (J) | Minimum Cost Duration (s) | Preferred Duraiton (s) | |
|---|---|---|---|---|
| a1 | 2.506 | 25.58113 | 0.8518398 | 0.7806626 |
| a1 | 3.959 | 27.28208 | 0.9084598 | 0.8441430 |
| a1 | 4.894 | 28.10861 | 0.9359942 | 0.8676516 |
| a1 | 6.282 | 29.11412 | 0.9694671 | 0.9044893 |
| Speed = 1 | Speed = 2 | Speed = 3 | Speed = 4 | Speed = 5 | Speed = 6 | Speed = 7 | |
|---|---|---|---|---|---|---|---|
| 2.73 kg | 0.5486 ± 0.014 | 0.6202 ± 0.0211 | 0.7576 ± 0.0325 | 0.951 ± 0.0419 | 1.1227 ± 0.0476 | 1.2528 ± 0.04 | NaN ± NA |
| 4.83 kg | 0.5644 ± 0.0145 | 0.6295 ± 0.0219 | 0.7677 ± 0.0355 | 0.9386 ± 0.0381 | 1.1305 ± 0.0416 | 1.2593 ± 0.0459 | NaN ± NA |
| 7.13 kg | NaN ± NA | 0.5921 ± 0.011 | 0.6819 ± 0.007 | 0.8569 ± 0.0082 | 1.0306 ± 0.0152 | 1.2143 ± 0.0205 | 1.3931 ± 0.0269 |
| 11.69 kg | NaN ± NA | 0.6114 ± 0.0113 | 0.6931 ± 0.0115 | 0.8638 ± 0.0102 | 1.0304 ± 0.0163 | 1.2184 ± 0.0144 | 1.38 ± 0.013 |
##
## Simultaneous Tests for General Linear Hypotheses
##
## Fit: lmer(formula = log(miss_dist) ~ log(movedur) + eff_mass2 + (1 |
## subj), data = metdata)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) == 0 -5.529646 0.058862 -93.94 <2e-16 ***
## log(movedur) == 0 -0.937237 0.017751 -52.80 <2e-16 ***
## eff_mass2 == 0 0.021596 0.001683 12.83 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
| Speed = 1 | Speed = 2 | Speed = 3 | Speed = 4 | Speed = 5 | Speed = 6 | Speed = 7 | |
|---|---|---|---|---|---|---|---|
| 2.73 kg | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA |
| 4.83 kg | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA |
| 7.13 kg | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA |
| 11.69 kg | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA |
## `geom_smooth()` using formula = 'y ~ x'
Figure 2.5: Endpoint Error.
##
## Simultaneous Tests for General Linear Hypotheses
##
## Fit: lmer(formula = log(missangle) ~ log(movedur) + eff_mass + (1 |
## subj), data = c)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) == 0 0.725112 0.110989 6.533 6.44e-11 ***
## log(movedur) == 0 -1.140494 0.074464 -15.316 < 2e-16 ***
## eff_mass == 0 0.017010 0.006734 2.526 0.0115 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
| Speed = 1 | Speed = 2 | Speed = 3 | Speed = 4 | Speed = 5 | Speed = 6 | Speed = 7 | |
|---|---|---|---|---|---|---|---|
| 2.73 kg | 1.1816±,0.3227 | 0.8386±,0.3227 | 0.7531±,0.3227 | 0.5641±,0.3227 | 0.4743±,0.3227 | 0.4589±,0.3227 | 0.5233±,0.3227 |
| 4.83 kg | 1.2879±,0.3506 | 0.9431±,0.3506 | 0.7494±,0.3506 | 0.6479±,0.3506 | 0.5246±,0.3506 | 0.5009±,0.3506 | 0.547±,0.3506 |
| 7.13 kg | ±, | 1.0496±,0.3291 | 0.8785±,0.3291 | 0.652±,0.3291 | 0.511±,0.3291 | 0.4353±,0.3291 | 0.4983±,0.3291 |
| 11.69 kg | ±, | 1.2156±,0.3427 | 0.9214±,0.3427 | 0.6676±,0.3427 | 0.53±,0.3427 | 0.452±,0.3427 | 0.493±,0.3427 |
## `geom_smooth()` using formula = 'y ~ x'
Figure 2.6: Angular miss variance.
##
## Simultaneous Tests for General Linear Hypotheses
##
## Fit: lmer(formula = log(miss_rad) ~ log(movedur) + eff_mass + (1 |
## subj), data = c)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) == 0 -10.560240 0.086391 -122.237 <2e-16 ***
## log(movedur) == 0 -1.000088 0.070361 -14.214 <2e-16 ***
## eff_mass == 0 -0.006766 0.006364 -1.063 0.288
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
| Speed = 1 | Speed = 2 | Speed = 3 | Speed = 4 | Speed = 5 | Speed = 6 | Speed = 7 | |
|---|---|---|---|---|---|---|---|
| 2.73 kg | 0.3286±,0.0772 | 0.2452±,0.0943 | 0.212±,0.056 | 0.1659±,0.0119 | 0.1802±,0.0322 | 0.1666±,0.0096 | 0.1983±,0.0012 |
| 4.83 kg | 0.3244±,0.0778 | 0.2426±,0.0473 | 0.1943±,0.0302 | 0.1928±,0.0334 | 0.1793±,0.023 | 0.1752±,0.012 | 0.183±,0.0184 |
| 7.13 kg | ±, | 0.2456±,0.0572 | 0.2012±,0.0684 | 0.1834±,0.0723 | 0.1603±,0.0278 | 0.1578±,0.014 | 0.1647±,0.0191 |
| 11.69 kg | ±, | 0.2745±,0.0397 | 0.1985±,0.013 | 0.1776±,0.0235 | 0.1613±,0.0264 | 0.1564±,0.0164 | 0.1619±,0.0177 |
## `geom_smooth()` using formula = 'y ~ x'
Figure 2.7: Radial miss variance.
##
## Simultaneous Tests for General Linear Hypotheses
##
## Fit: lmer(formula = reaction_tanv ~ log(movedur) + eff_mass2 + (1 |
## subj), data = metdata)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) == 0 0.1585730 0.0071557 22.16 <2e-16 ***
## log(movedur) == 0 0.0530319 0.0012279 43.19 <2e-16 ***
## eff_mass2 == 0 0.0023967 0.0001164 20.59 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
##
## Simultaneous Tests for General Linear Hypotheses
##
## Fit: lmer(formula = reaction_tanv ~ movedur + eff_mass2 + (1 | subj),
## data = metdata)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) == 0 0.0924072 0.0072719 12.71 <2e-16 ***
## movedur == 0 0.0643985 0.0014023 45.92 <2e-16 ***
## eff_mass2 == 0 0.0023962 0.0001155 20.75 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
| Speed = 1 | Speed = 2 | Speed = 3 | Speed = 4 | Speed = 5 | Speed = 6 | Speed = 7 | |
|---|---|---|---|---|---|---|---|
| 2.73 kg | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA |
| 4.83 kg | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA |
| 7.13 kg | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA |
| 11.69 kg | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA |
## `geom_smooth()` using formula = 'y ~ x'
Figure 2.8: Reaction time in metabolic experiment.
##
## Simultaneous Tests for General Linear Hypotheses
##
## Fit: lmer(formula = reaction_tanv_perc ~ log(movedur) + eff_mass2 +
## (1 | subj), data = metdata)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) == 0 0.1563571 0.0092862 16.84 <2e-16 ***
## log(movedur) == 0 -0.1432859 0.0016273 -88.05 <2e-16 ***
## eff_mass2 == 0 0.0028230 0.0001543 18.30 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
##
## Simultaneous Tests for General Linear Hypotheses
##
## Fit: lmer(formula = reaction_tanv_perc ~ movedur + eff_mass2 + (1 |
## subj), data = metdata)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) == 0 0.3192568 0.0093404 34.18 <2e-16 ***
## movedur == 0 -0.1536866 0.0019291 -79.67 <2e-16 ***
## eff_mass2 == 0 0.0025781 0.0001589 16.23 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
| Speed = 1 | Speed = 2 | Speed = 3 | Speed = 4 | Speed = 5 | Speed = 6 | Speed = 7 | |
|---|---|---|---|---|---|---|---|
| 2.73 kg | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA |
| 4.83 kg | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA |
| 7.13 kg | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA |
| 11.69 kg | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA | NaN ± NA |
## `geom_smooth()` using formula = 'y ~ x'
Figure 2.9: Reaction time in metabolic experiment.
Figure 2.10: Metabolic experiment results.
We compute 4 effort models here. Gross metabolics, net metabolics, and sum of torque squared (experimentally calculated and calcualted from minimum jerk). Net and gross metabolics have been addressed before, here we add sum of torque squared.
Sum of torque squared is calcualted from the data and simulated minimum jerk profiles and then fit to an effort model like net metabolic and gross metabolic power but without the a parameter.
\[ \dot{e} = \frac{bm^c}{T_m^d} \]
The parameters fit for the effort models are shown in table @ref(tab:effort_prarms).
Figure 3.1: Sum of torque squared fits from the data
This table shows a summary of all the parameters that were fitted in the effort models. SSE, AIC, and BIC can be found in their respective sections.
| Net Metabolics | Gross Metabolics | Torque\(^2\) | Torque\(^2\) minjerk | |
|---|---|---|---|---|
| a0 | 73.3259±3.6041 | 73.3259±3.6041 | 0 | 0 |
| a | 24.0346 ± 2.9124 | 98.2501 ± 3.0512 | 0 | 0 |
| b | 1.0308 ± 0.467 | 0.864 ± 0.4319 | 0.0136 ± 0.0028 | 0.0554 ± 0.0259 |
| c | 0.7964 ± 0.0904 | 0.8308 ± 0.0998 | 2.3415 ± 0.0706 | 2.2988 ± 0.1687 |
| d | 5.6574 ± 0.5473 | 5.8254 ± 0.603 | 5.0157 ± 0.1792 | 1.2333 ± 0.0614 |
| SSE | 105365.400000357 | 120872.749595644 | 1509.56505066476 | 118250.243680345 |
| AIC | 1725.15615301424 | 1750.8320060654 | 853.626308139953 | 1917.62664958662 |
| BIC | 1741.31169609851 | 1766.98754914967 | 866.122164057567 | 1930.97680190542 |
Sum of torque squared is calculated from the data and simulated minimum jerk profiles and then fit to an effort model like net metabolic and gross metabolic power. In these we allowed \(a\) to be fit to see if it would predict a 0 offset.
\[ \dot{e} = a+\frac{bm^c}{T_m^d} \]
This table shows the confident intervals on the torque with \(a\) model. The probability of \(a\) (\(a_1\)) being greater than 0 is 0.0015173.
| 2.5% | 97.5% | |
|---|---|---|
| a1 | -1.2296995 | 0.2214529 |
| a2 | 0.0100917 | 0.0294421 |
| a3 | 2.1176112 | 2.4417127 |
| a4 | 4.4647333 | 5.2767459 |
The probability function for the 2a is: \[ ln\left(\frac{P_i}{1-P_i}\right) = \beta_0 + \beta_1 x_1 \] Which leads to \[ P(Success|T) = \frac{1}{1+e^{-(\beta_0) - (\beta_1)T}} \] Mass is removed from this probability as according to the model it is insignificant. Duration and mass also conditions here, so we only use duration. I leave it \(\beta_1\) because that is more similar to the glm with mass from experiment 1.
We then use this function to first fit an inverse logit to experiment 2a and 2b. We then use the criteria for success and fit the same inverse logit function but using the data from experiment 1.
The following table shows the beta coefficients for the inverse logit function only predicting from experiment 2a and 2b.
| 2a | 2b | |
|---|---|---|
| \(\beta_0\) | 3.3276 ± 0.264 | 1.8785 ± 0.125 |
| \(\beta_1\) | -0.1023 ± 0.303 | -0.4024 ± 0.133 |
Using these functions we can then predict the probability of success as a fraction of success given the data and using the logit model. The following table shows this for experiment 2a and 2b.
| 2a | Predicted 2a | 2b | Predicted 2b | |
|---|---|---|---|---|
| 2.506 | 0.9606 | 0.9626 | 0.7928 | 0.8232 |
| 3.959 | 0.9623 | 0.9624 | 0.8487 | 0.8199 |
| 4.894 | 0.9612 | 0.9623 | 0.8083 | 0.8184 |
| 6.282 | 0.9651 | 0.9621 | 0.8260 | 0.8156 |
We can also estimate the probability on the standard deviation of the miss distance.
| 2a | Predicted 2a | 2b | Predicted 2b | |
|---|---|---|---|---|
| 2.506 | 0.9606 | 0.9797 | 0.7928 | 0.9797 |
| 3.959 | 0.9623 | 0.9772 | 0.8487 | 0.9772 |
| 4.894 | 0.9612 | 0.9780 | 0.8083 | 0.9780 |
| 6.282 | 0.9651 | 0.9805 | 0.8260 | 0.9805 |
The plot below shows the fits of the glm’s fitted to only data from experiment 2a and 2b. Unfortunately, these glm’s don’t seem to have the same behavior as data fitted to experiment 1 of dropping off to 0 at faster speeds. This is probably due to the lack of really fast or really slow trials so it just predicts a flat line essentially.
Figure 4.1: Probability of success with glm fitted to experiment 2a and 2b data.
\[ P(Success|T) = \frac{1}{1+e^{-(\beta_0) - (\beta_1)T - (\beta_2)m}} \]
This table shows the beta coefficients when using an inverse logit on experiment 1 trying to predict 2a and 2b.
| 2a | 2b | |
|---|---|---|
| \(\beta_0\) | -1.4496 ± 0.125 | -2.9312 ± 0.091 |
| \(\beta_1\) | 5.8768 ± 0.188 | 6.0912 ± 0.129 |
| \(\beta_2\) | -0.0946 ± 0.008 | -0.0828 ± 0.006 |
This plot only includes movement durations that are seen in the metabolic experiment. The black vertical bars show the range of durations for the 2a preferred exerpiement. The red vertical bars show the range of durations for the smallt target.
Figure 4.2: Probability of success given movement duration and mass. The black vertical bars show the range of durations for the 2a preferred exerpiement. The red vertical bars show the range of durations for the smallt target.
This plot includes low and high movement durations to show that the functions converge to 0 and 1 probability respectively.
Figure 4.3: Probability of success given movement duration and mass. The black vertical bars show the range of durations for the 2a preferred exerpiement. The red vertical bars show the range of durations for the smallt target.
This next table shows the movement durations for experiment 2a and 2b, the probability of success from the experiment, along with the probability of success from the logistic regression. The last row is the mean probability.
| 2a Movedur | 2a Exp Prob | 2a Pred Prob | 2b Movedur | 2b Exp Prob | 2b Pred Prob | |
|---|---|---|---|---|---|---|
| 2.506 | 0.7807 | 0.9606 | 0.9479 | 0.8457 | 0.7928 | 0.8821 |
| 3.959 | 0.8441 | 0.9623 | 0.9584 | 0.9018 | 0.8487 | 0.9033 |
| 4.894 | 0.8677 | 0.9612 | 0.9603 | 0.9262 | 0.8083 | 0.9093 |
| 6.282 | 0.9045 | 0.9651 | 0.9634 | 0.9733 | 0.8260 | 0.9225 |
| Mean | NaN | 0.9623 | 0.9575 | NaN | 0.8189 | 0.9043 |
The table (@ref{tab:optdurprob}) shows the metabolically optimal (gross) durations with the predicted probabilities from the glm using experiment 1 and 2a.
| Effective.Mass | Duration | Success.Prob |
|---|---|---|
| 2.44 | 0.6627202 | 0.9015146 |
| 4.83 | 0.7073980 | 0.9046978 |
| 7.13 | 0.7291192 | 0.8966490 |
| 11.69 | 0.7555548 | 0.8681094 |
The probability of reward that minimizes the error of predicted movement durations for the 2a experiment is 0.958. The table below shows the predicted movement durations and the expected movement durations. The SSE of this prediction is 0.0021639.
| Effective Mass (kg) | Predicted Duration | Preferred Duration | |
|---|---|---|---|
| 2.506 | 0.819 | 0.78 | |
| 3.959 | 0.843 | 0.843 | |
| 4.894 | 0.858 | 0.867 | |
| 6.282 | 0.88 | 0.904 |
The probability of reward that minimizes the error of predicted movement durations for the 2a experiment is 0.9053. The table below shows hte predicted movement durations and the expected movement durations. The SSE of this prediction is 0.017531.
| Effective Mass (kg) | Predicted Duration | Preferred Duration | |
|---|---|---|---|
| 2.506 | 0.886 | 0.846 | |
| 3.959 | 0.906 | 0.902 | |
| 4.894 | 0.919 | 0.927 | |
| 6.282 | 0.938 | 0.973 |
This plot below shows individual subjects and their utility fits. This uses gross metabolics as the effort term.
The average fitted \(\alpha\) value was 48.1075.
Figure 5.1: Utility fits by subject.
We next fitted a utility model by altering \(\alpha\) to try and predict the movement durations seen in 2a,b,c.
The utility function that is fit for these next plots is below. \(T_r\) and \(T_m\) are the reaction time and movement duration. \(P(R|m,t)\) is determined from the section above, probability alpha modeling. \(a\), \(b\), \(c\), \(d\) are determined from the metabolic data. Resting rate is shown by \(a_0\), and \(a_0\) = 73.527. The parameters a, b, c, and d are shown in 3.1.
\[J = \frac{\alpha P(R|m,T_m) -\left( a_0 T_r + a T_m + \frac{bm^c}{T_m^d} \right)}{T_r+T_m}\] Ideally the probability function has an effect of mass in it, but for the following results we use the glm from experiment 2a/2b to fit \(\alpha\), which leads to the probability function only including a term of time.
\[J = \frac{\alpha P(R|T_m) -\left( a_0 T_r + a T_m + \frac{bm^c}{T_m^d} \right)}{T_r+T_m}\]
\(T_r\) and \(T_m\) are the reaction time and movement duration. Using the values from experiment 2a,b,c, we can optimize the error of the prediction by altering \(\alpha\).
The tables below show the movement durations (@ref{tab:utilmovedurstab}), reaction time (@ref{rab:utilreacttimestab}).
| 2a | 2b | 2c | |
|---|---|---|---|
| 2.506 kg | 0.781 | 0.846 | 0.667 |
| 3.959 kg | 0.844 | 0.902 | 0.743 |
| 4.894 kg | 0.868 | 0.926 | 0.782 |
| 6.282 kg | 0.904 | 0.973 | 0.823 |
| 2a | 2b | 2c | |
|---|---|---|---|
| 2.506 kg | 0.184 | 0.208 | 0.201 |
| 3.959 kg | 0.194 | 0.217 | 0.214 |
| 4.894 kg | 0.198 | 0.220 | 0.219 |
| 6.282 kg | 0.203 | 0.232 | 0.223 |
FITTING Three ALPHA VALUEs, one to each experiment. ### 2a Alpha This table (??) shows the \(\alpha\) value, predicted duration for the models, and the SSE between that and the experimental data. The SSE for all these models is shown in detail later.
| 2a Experiment | Net Metabolic Power | Gross Metabolic power | Utility (Net Power) | Utility (Gross Power | Torque\(^2\) | Torque\(^2\) minjerk | |
|---|---|---|---|---|---|---|---|
| Alpha | 0 | 0 | 0 | 79.4094 | 54.4634 | 1.3106 | 31.1648 |
| 2.44 | 0.7807 | 0.8561 | 0.6627 | 0.785 | 0.785 | 0.617 | 0.74 |
| 4.83 | 0.8441 | 0.913 | 0.7074 | 0.84 | 0.84 | 0.777 | 0.81 |
| 7.13 | 0.8677 | 0.9407 | 0.7291 | 0.868 | 0.868 | 0.867 | 0.86 |
| 11.69 | 0.9045 | 0.9743 | 0.7556 | 0.903 | 0.903 | 0.989 | 0.96 |
| SSE | 0 | 2.064e-02 | 7.398e-02 | 3.832e-05 | 3.832e-05 | 3.844e-02 | 5.959e-03 |
The probability of success for utility in experiement 2a using the optimized alpha value are shown below.
| Utility Net | Utility Gross | Utility Torque | Utility Torque Mj | |
|---|---|---|---|---|
| 2.506 | 0.9491427 | 0.9491427 | 0.8742680 | 0.9347516 |
| 3.959 | 0.9573953 | 0.9573953 | 0.9394607 | 0.9495951 |
| 4.894 | 0.9603922 | 0.9603922 | 0.9601680 | 0.9585646 |
| 6.282 | 0.9631249 | 0.9631249 | 0.9774244 | 0.9733414 |
This table (5.5) shows the \(\alpha\) value, predicted durations for the models, and the SSE between that and the experimental data. The SSE for all these models is shown in detail later (section @ref{SSE2b}).
| 2b Experiment | Net Metabolic Power | Gross Metabolic power | Utility (Net Power) | Utility (Gross Power | Torque\(^2\) | Torque\(^2\) minjerk | |
|---|---|---|---|---|---|---|---|
| Alpha | 0 | 0 | 0 | 141.2476 | 80.2642 | 28.0457 | 98.0839 |
| 2.44 | 0.8457 | 0.8561 | 0.6627 | 0.865 | 0.862 | 0.75 | 0.85 |
| 4.83 | 0.9018 | 0.913 | 0.7074 | 0.904 | 0.904 | 0.803 | 0.88 |
| 7.13 | 0.9262 | 0.9407 | 0.7291 | 0.925 | 0.927 | 0.838 | 0.9 |
| 11.69 | 0.9733 | 0.9743 | 0.7556 | 0.955 | 0.958 | 0.889 | 0.93 |
| SSE | 0 | 4.426e-04 | 1.575e-01 | 7.144e-04 | 5.057e-04 | 3.381e-02 | 3.058e-03 |
The probability of success for utility in experiement 2b using the optimized alpha value are shown below.
| Utility Net | Utility Gross | Utility Torque | Utility Torque Mj | |
|---|---|---|---|---|
| 2.506 | 0.8938010 | 0.8920540 | 0.8068510 | 0.8848110 |
| 3.959 | 0.9044274 | 0.9044274 | 0.8364710 | 0.8910223 |
| 4.894 | 0.9087040 | 0.9097096 | 0.8542056 | 0.8952598 |
| 6.282 | 0.9141757 | 0.9155986 | 0.8769327 | 0.9014499 |
This table (5.7) shows the \(\alpha\) value, predicted durations for the models, and the SSE between that and the experimental data. The SSE for all these models is shown in detail later (section @ref{SSE2b}).
| 2c Experiment | Net Metabolic Power | Gross Metabolic power | Utility (Net Power) | Utility (Gross Power | Torque\(^2\) | Torque\(^2\) minjerk | |
|---|---|---|---|---|---|---|---|
| Alpha | 0 | 0 | 0 | 94.0121 | 75.1132 | 25.1875 | 22.0569 |
| 2.44 | 0.6673 | 0.8561 | 0.6627 | 0.692 | 0.691 | 0.529 | 0.01 |
| 4.83 | 0.7429 | 0.913 | 0.7074 | 0.748 | 0.746 | 0.694 | 0.05 |
| 7.13 | 0.7816 | 0.9407 | 0.7291 | 0.776 | 0.773 | 0.785 | 0.12 |
| 11.69 | 0.8234 | 0.9743 | 0.7556 | 0.811 | 0.807 | 0.927 | 0.88 |
| SSE | 0 | 1.127e-01 | 8.635e-03 | 8.203e-04 | 9.131e-04 | 3.227e-02 | 1.353e+00 |
The probability of success for utility in experiement 2b using the optimized alpha value are shown below.
| Utility Net | Utility Gross | Utility Torque | Utility Torque Mj | |
|---|---|---|---|---|
| 2.506 | 1 | 1 | 1 | 1 |
| 3.959 | 1 | 1 | 1 | 1 |
| 4.894 | 1 | 1 | 1 | 1 |
| 6.282 | 1 | 1 | 1 | 1 |
Figure 5.2: Utility fits across experiments.
This section analysis fits one \(\alpha\) value to experiment 2a and 2b at the same time. These next tables show the movement durations, predicted movement durations, the fitted alpha values, and the probabilities of success. The \(\alpha\) value for 2a and 2b are fit at once, so it is the same. 2c has its own \(\alpha\) value.
The \(\alpha\) value fitted here is 60.6779456. The SSE for experiment 2a/2b when using one alpha is 2.632e-03. The SSE for experiment 2c is 9.131e-04. The total SSE for all 3 is 3.545e-03.
| 2a Exp | 2a pred | 2b Exp | 2b pred | 2c Exp | 2c pred | |
|---|---|---|---|---|---|---|
| 2.506 | 0.7806626 | 0.774 | 0.8456631 | 0.878 | 0.6673158 | 0.691 |
| 3.959 | 0.8441430 | 0.828 | 0.9018428 | 0.923 | 0.7428759 | 0.746 |
| 4.894 | 0.8676516 | 0.855 | 0.9262331 | 0.947 | 0.7815969 | 0.773 |
| 6.282 | 0.9044893 | 0.890 | 0.9732835 | 0.979 | 0.8233858 | 0.807 |
| 2a | 2b | 2c | |
|---|---|---|---|
| 2.506 | 0.9459 | 0.9011 | 1 |
| 3.959 | 0.9544 | 0.9140 | 1 |
| 4.894 | 0.9574 | 0.9192 | 1 |
| 6.282 | 0.9603 | 0.9250 | 1 |
| 2a | 2b | 2c | |
|---|---|---|---|
| lpha | 60.678 | 60.678 | 75.113 |
Figure 5.3: Utility fits across experiments.
Utility 1: \[J = \frac{\alpha P(R|m,T_m) -\left( a_0 T_r + a T_m + \frac{bm^c}{T_m^d} \right)}{T_r+T_m}\]
Utility 2: \[J = \alpha P(R|m,T_m) -\left( a_0 T_r + a T_m + \frac{bm^c}{T_m^d} \right)\]
Utility 3: \[J = \frac{\alpha P(R|m,T_m)}{T_r+T_m} -\left( a_0 T_r + a T_m + \frac{bm^c}{T_m^d} \right)\]
Utility 4: \[J = \frac{P(R|m,T_m)}{a_0 T_r + a T_m + \frac{bm^c}{T_m^d}}\]
| eff_mass | Movement Duration (s) | Utility 1 Gross Duration | Utility 2 Gross Duration | Utility 3 Gross Duration | Utility 1 Net Duration | Utility 2 Net Duration | Utility 3 Net Duration | Utility Comb 1 Gross Duration | Utility Comb 2 Gross Duration | Utility Comb 3 Gross Duration | Utility Comb 1 Net Duration | Utility Comb 2 Net Duration | Utility Comb 3 Net Duration |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| alpha | alpha | 54.463 | 259.211 | -94.223 | 79.409 | -59.453 | 21.098 | 60.678 | 166.74 | 3.149 | 93.503 | -7.803 | 20.122 |
| 2.506 | 0.7807 | 0.785 | 0.804 | 0.809 | 0.785 | 0.777 | 0.785 | 0.774 | 0.76 | 0.66 | 0.764 | 0.846 | 0.788 |
| 3.959 | 0.8441 | 0.84 | 0.84 | 0.841 | 0.84 | 0.841 | 0.842 | 0.828 | 0.799 | 0.705 | 0.816 | 0.904 | 0.844 |
| 4.894 | 0.8677 | 0.868 | 0.86 | 0.857 | 0.868 | 0.871 | 0.87 | 0.855 | 0.819 | 0.727 | 0.843 | 0.932 | 0.872 |
| 6.282 | 0.9045 | 0.903 | 0.886 | 0.875 | 0.903 | 0.906 | 0.904 | 0.89 | 0.846 | 0.753 | 0.877 | 0.966 | 0.907 |
| SSE | SSE | 3.832e-05 | 9.622e-04 | 1.796e-03 | 3.832e-05 | 3.679e-05 | 2.916e-05 | 6.750e-04 | 8.253e-03 | 7.665e-02 | 2.433e-03 | 1.578e-02 | 7.907e-05 |
| eff_mass | Movement Duration (s) | Utility 1 Gross Duration | Utility 2 Gross Duration | Utility 3 Gross Duration | Utility 1 Net Duration | Utility 2 Net Duration | Utility 3 Net Duration | Utility Comb 1 Gross Duration | Utility Comb 2 Gross Duration | Utility Comb 3 Gross Duration | Utility Comb 1 Net Duration | Utility Comb 2 Net Duration | Utility Comb 3 Net Duration |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| alpha | alpha | 80.264 | 142.685 | 982.678 | 141.248 | -2.762 | 5.921 | 60.678 | 166.74 | 3.149 | 93.503 | -7.803 | 20.122 |
| 2.506 | 0.8457 | 0.862 | 0.875 | 0.764 | 0.865 | 0.846 | 0.849 | 0.878 | 0.899 | 0.665 | 0.897 | 0.826 | 0.836 |
| 3.959 | 0.9018 | 0.904 | 0.905 | 0.793 | 0.904 | 0.904 | 0.903 | 0.923 | 0.928 | 0.709 | 0.939 | 0.886 | 0.887 |
| 4.894 | 0.9262 | 0.927 | 0.922 | 0.81 | 0.925 | 0.932 | 0.93 | 0.947 | 0.944 | 0.731 | 0.962 | 0.915 | 0.912 |
| 6.282 | 0.9733 | 0.958 | 0.945 | 0.835 | 0.955 | 0.966 | 0.964 | 0.979 | 0.967 | 0.757 | 0.994 | 0.949 | 0.945 |
| SSE | SSE | 5.057e-04 | 1.688e-03 | 5.115e-02 | 7.144e-04 | 9.107e-05 | 1.128e-04 | 1.957e-03 | 3.884e-03 | 1.547e-01 | 5.725e-03 | 1.354e-03 | 1.316e-03 |
| eff_mass | Movement Duration (s) | Utility 1 Gross Duration | Utility 2 Gross Duration | Utility 3 Gross Duration | Utility 1 Net Duration | Utility 2 Net Duration | Utility 3 Net Duration | Utility Comb 1 Gross Duration | Utility Comb 2 Gross Duration | Utility Comb 3 Gross Duration | Utility Comb 1 Net Duration | Utility Comb 2 Net Duration | Utility Comb 3 Net Duration |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| alpha | alpha | 75.113 | 99999.997 | -23.62 | 94.012 | 99999.997 | 47.789 | 60.678 | 166.74 | 3.149 | 93.503 | -7.803 | 20.122 |
| 2.506 | 0.6673 | 0.691 | 0.663 | 0.703 | 0.692 | 0.856 | 0.686 | 0.719 | 0.663 | 0.658 | 0.693 | 0.856 | 0.765 |
| 3.959 | 0.7429 | 0.746 | 0.707 | 0.745 | 0.748 | 0.913 | 0.746 | 0.776 | 0.707 | 0.703 | 0.749 | 0.913 | 0.825 |
| 4.894 | 0.7816 | 0.773 | 0.729 | 0.766 | 0.776 | 0.941 | 0.774 | 0.804 | 0.729 | 0.725 | 0.777 | 0.941 | 0.854 |
| 6.282 | 0.8234 | 0.807 | 0.756 | 0.79 | 0.811 | 0.974 | 0.811 | 0.839 | 0.756 | 0.751 | 0.812 | 0.974 | 0.89 |
| SSE | SSE | 1.031e-01 | 1.039e-01 | 1.280e-02 | 1.029e-01 | 1.008e-01 | 1.004e-01 | 4.514e-03 | 8.613e-03 | 1.012e-02 | 8.479e-04 | 1.126e-01 | 2.597e-02 |
Figure 6.1: SSE Alternative utility models for 2a, 2b, and 2c.
Figure 6.2: SSE Alternative utility models for 2a, 2b, and 2c.
| eff_mass | Movement Duration (s) | Utility 1 Gross Duration | Utility 2 Gross Duration | Utility 3 Gross Duration | Utility 1 Net Duration | Utility 2 Net Duration | Utility 3 Net Duration | Utility Comb 1 Gross Duration | Utility Comb 2 Gross Duration | Utility Comb 3 Gross Duration | Utility Comb 1 Net Duration | Utility Comb 2 Net Duration | Utility Comb 3 Net Duration |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| alpha | alpha | 54.463 | 259.211 | -94.223 | 79.409 | -59.453 | 21.098 | 60.678 | 166.74 | 3.149 | 93.503 | -7.803 | 20.122 |
| 2.506 | 0.7807 | 0.785 | 0.804 | 0.809 | 0.785 | 0.777 | 0.785 | 0.774 | 0.76 | 0.66 | 0.764 | 0.846 | 0.788 |
| 3.959 | 0.8441 | 0.84 | 0.84 | 0.841 | 0.84 | 0.841 | 0.842 | 0.828 | 0.799 | 0.705 | 0.816 | 0.904 | 0.844 |
| 4.894 | 0.8677 | 0.868 | 0.86 | 0.857 | 0.868 | 0.871 | 0.87 | 0.855 | 0.819 | 0.727 | 0.843 | 0.932 | 0.872 |
| 6.282 | 0.9045 | 0.903 | 0.886 | 0.875 | 0.903 | 0.906 | 0.904 | 0.89 | 0.846 | 0.753 | 0.877 | 0.966 | 0.907 |
| SSE | SSE | 3.832e-05 | 9.622e-04 | 1.796e-03 | 3.832e-05 | 3.679e-05 | 2.916e-05 | 6.750e-04 | 8.253e-03 | 7.665e-02 | 2.433e-03 | 1.578e-02 | 7.907e-05 |
| eff_mass | Movement Duration (s) | Utility 1 Gross Duration | Utility 2 Gross Duration | Utility 3 Gross Duration | Utility 1 Net Duration | Utility 2 Net Duration | Utility 3 Net Duration | Utility Comb 1 Gross Duration | Utility Comb 2 Gross Duration | Utility Comb 3 Gross Duration | Utility Comb 1 Net Duration | Utility Comb 2 Net Duration | Utility Comb 3 Net Duration |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| alpha | alpha | 80.264 | 142.685 | 982.678 | 141.248 | -2.762 | 5.921 | 60.678 | 166.74 | 3.149 | 93.503 | -7.803 | 20.122 |
| 2.506 | 0.8457 | 0.862 | 0.875 | 0.764 | 0.865 | 0.846 | 0.849 | 0.878 | 0.899 | 0.665 | 0.897 | 0.826 | 0.836 |
| 3.959 | 0.9018 | 0.904 | 0.905 | 0.793 | 0.904 | 0.904 | 0.903 | 0.923 | 0.928 | 0.709 | 0.939 | 0.886 | 0.887 |
| 4.894 | 0.9262 | 0.927 | 0.922 | 0.81 | 0.925 | 0.932 | 0.93 | 0.947 | 0.944 | 0.731 | 0.962 | 0.915 | 0.912 |
| 6.282 | 0.9733 | 0.958 | 0.945 | 0.835 | 0.955 | 0.966 | 0.964 | 0.979 | 0.967 | 0.757 | 0.994 | 0.949 | 0.945 |
| SSE | SSE | 5.057e-04 | 1.688e-03 | 5.115e-02 | 7.144e-04 | 9.107e-05 | 1.128e-04 | 1.957e-03 | 3.884e-03 | 1.547e-01 | 5.725e-03 | 1.354e-03 | 1.316e-03 |
| eff_mass | Movement Duration (s) | Utility 1 Gross Duration | Utility 2 Gross Duration | Utility 3 Gross Duration | Utility 1 Net Duration | Utility 2 Net Duration | Utility 3 Net Duration | Utility Comb 1 Gross Duration | Utility Comb 2 Gross Duration | Utility Comb 3 Gross Duration | Utility Comb 1 Net Duration | Utility Comb 2 Net Duration | Utility Comb 3 Net Duration |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| alpha | alpha | 75.113 | 99999.997 | -23.62 | 94.012 | 99999.997 | 47.789 | 75.113 | 99999.997 | -23.62 | 94.012 | 99999.997 | 47.789 |
| 2.506 | 0.6673 | 0.691 | 0.663 | 0.703 | 0.692 | 0.856 | 0.686 | 0.691 | 0.663 | 0.703 | 0.692 | 0.856 | 0.686 |
| 3.959 | 0.7429 | 0.746 | 0.707 | 0.745 | 0.748 | 0.913 | 0.746 | 0.746 | 0.707 | 0.745 | 0.748 | 0.913 | 0.746 |
| 4.894 | 0.7816 | 0.773 | 0.729 | 0.766 | 0.776 | 0.941 | 0.774 | 0.773 | 0.729 | 0.766 | 0.776 | 0.941 | 0.774 |
| 6.282 | 0.8234 | 0.807 | 0.756 | 0.79 | 0.811 | 0.974 | 0.811 | 0.807 | 0.756 | 0.79 | 0.811 | 0.974 | 0.811 |
| SSE | SSE | 1.031e-01 | 1.039e-01 | 1.280e-02 | 1.029e-01 | 1.008e-01 | 1.004e-01 | 9.131e-04 | 8.613e-03 | 2.636e-03 | 8.203e-04 | 1.126e-01 | 5.700e-04 |
Figure 6.3: SSE Alternative utility models for 2a, 2b, and 2c.
Figure 6.4: SSE Alternative utility models for 2a, 2b, and 2c.
This next plot/section is showing the total SSE when fitting one alpha to 2a/2b, then applied to 2c.
| Experimental | Utility Gross | Utility Net | Utility Torque | Net Reward | Effeciency | Gross Cost | Net Cost | |
|---|---|---|---|---|---|---|---|---|
| 2.506 | 0.7807 | 0.7740 | 0.7640 | 0.6030 | 0.7600 | 0.7230 | 0.6627 | 0.8561 |
| 3.959 | 0.8441 | 0.8280 | 0.8160 | 0.7500 | 0.7990 | 0.7680 | 0.7074 | 0.9130 |
| 4.894 | 0.8677 | 0.8550 | 0.8430 | 0.8330 | 0.8190 | 0.7900 | 0.7291 | 0.9407 |
| 6.282 | 0.9045 | 0.8900 | 0.8770 | 0.9450 | 0.8460 | 0.8190 | 0.7556 | 0.9743 |
| SSE | 0.0000 | 0.0007 | 0.0024 | 0.0433 | 0.0083 | 0.0225 | 0.0740 | 0.0206 |
| Experimental 2b | Utility Gross | Utility Net | Utility Torque | Net Reward | Effeciency | Gross Cost | Net Cost | |
|---|---|---|---|---|---|---|---|---|
| 2.506 | 0.8457 | 0.878 | 0.8970 | 0.6570 | 0.8990 | 0.844 | 0.6627 | 0.8561 |
| 3.959 | 0.9018 | 0.923 | 0.9390 | 0.7940 | 0.9280 | 0.881 | 0.7074 | 0.9130 |
| 4.894 | 0.9262 | 0.947 | 0.9620 | 0.8680 | 0.9440 | 0.901 | 0.7291 | 0.9407 |
| 6.282 | 0.9733 | 0.979 | 0.9940 | 0.9650 | 0.9670 | 0.929 | 0.7556 | 0.9743 |
| SSE | 0.0000 | 0.002 | 0.0057 | 0.0507 | 0.0039 | 0.003 | 0.1575 | 0.0004 |
| Experimental 2c | Utility Gross | Utility Net | Utility Torque | Net Reward | Effeciency | Gross Cost | Net Cost | |
|---|---|---|---|---|---|---|---|---|
| 2.506 | 0.6673 | 0.7190 | 0.6930 | 0.5530 | 0.6630 | 0.6630 | 0.6627 | 0.8561 |
| 3.959 | 0.7429 | 0.7760 | 0.7490 | 0.7100 | 0.7070 | 0.7070 | 0.7074 | 0.9130 |
| 4.894 | 0.7816 | 0.8040 | 0.7770 | 0.7970 | 0.7290 | 0.7290 | 0.7291 | 0.9407 |
| 6.282 | 0.8234 | 0.8390 | 0.8120 | 0.9110 | 0.7560 | 0.7560 | 0.7556 | 0.9743 |
| SSE | 0.0000 | 0.0045 | 0.0008 | 0.0221 | 0.0086 | 0.0086 | 0.0086 | 0.1127 |
| exp | utnum | utmod | sse |
|---|---|---|---|
| 2a | 1 | Utility Gross | 0.0006750 |
| 2a | 2 | Utility Net | 0.0024330 |
| 2a | 3 | Utility Torque | 0.0432700 |
| 2a | 4 | Net Reward | 0.0082530 |
| 2a | 5 | Effeciency | 0.0224600 |
| 2a | 6 | Gross Cost | 0.0739800 |
| 2a | 7 | Net Cost | 0.0206400 |
| 2b | 1 | Utility Gross | 0.0019570 |
| 2b | 2 | Utility Net | 0.0057250 |
| 2b | 3 | Utility Torque | 0.0506800 |
| 2b | 4 | Net Reward | 0.0038840 |
| 2b | 5 | Effeciency | 0.0030350 |
| 2b | 6 | Gross Cost | 0.1575000 |
| 2b | 7 | Net Cost | 0.0004426 |
| 2c | 1 | Utility Gross | 0.0045140 |
| 2c | 2 | Utility Net | 0.0008479 |
| 2c | 3 | Utility Torque | 0.0220600 |
| 2c | 4 | Net Reward | 0.0086130 |
| 2c | 5 | Effeciency | 0.0086130 |
| 2c | 6 | Gross Cost | 0.0086350 |
| 2c | 7 | Net Cost | 0.1127000 |
| utmod | sse |
|---|---|
| Effeciency | 0.0341080 |
| Gross Cost | 0.2401150 |
| Net Cost | 0.1337826 |
| Net Reward | 0.0207500 |
| Utility Gross | 0.0071460 |
| Utility Net | 0.0090059 |
| Utility Torque | 0.1160100 |
| exp | utnum | utmod | sse |
|---|---|---|---|
| 2a | 1 | Utility Gross | 0.0002558 |
| 2a | 2 | Utility Net | 0.0003548 |
| 2a | 4 | Net Reward | 0.0041090 |
| 2a | 6 | Gross Cost | 0.0006631 |
| 2a | 7 | Net Cost | 0.0007998 |
| 2a | 3 | Utility Torque | 0.2662000 |
| 2a | 5 | Efficiency | 0.0005844 |
| 2b | 1 | Utility Gross | 0.0017960 |
| 2b | 2 | Utility Net | 0.0027340 |
| 2b | 4 | Net Reward | 0.0088790 |
| 2b | 6 | Gross Cost | 0.0001424 |
| 2b | 7 | Net Cost | 0.0001762 |
| 2b | 3 | Utility Torque | 0.1723000 |
| 2b | 5 | Efficiency | 0.0007889 |
| 2c | 1 | Utility Gross | 0.0084520 |
| 2c | 2 | Utility Net | 0.0074190 |
| 2c | 4 | Net Reward | 0.0161000 |
| 2c | 6 | Gross Cost | 0.0159500 |
| 2c | 7 | Net Cost | 0.0166100 |
| 2c | 3 | Utility Torque | 0.2730000 |
| 2c | 5 | Efficiency | 0.0161000 |
| utmod | sse |
|---|---|
| Efficiency | 0.0174733 |
| Gross Cost | 0.0167555 |
| Net Cost | 0.0175860 |
| Net Reward | 0.0290880 |
| Utility Gross | 0.0105038 |
| Utility Net | 0.0105078 |
| Utility Torque | 0.7115000 |
| Experimental Mvttimes | Utility Grs | Utility Net | Utility Torque | Net Rwd Grs | Efficiency | Gross Cost | Net Cost | |
|---|---|---|---|---|---|---|---|---|
| alpha | 54.463 | 79.409 | 1.311 | |||||
| 2.506 | 0.7807 | 0.785 | 0.785 | 0.617 | 0.804 | 0.723 | 0.6627 | 0.8561 |
| 3.959 | 0.8441 | 0.84 | 0.84 | 0.777 | 0.84 | 0.768 | 0.7074 | 0.913 |
| 4.894 | 0.8677 | 0.868 | 0.868 | 0.867 | 0.86 | 0.79 | 0.7291 | 0.9407 |
| 6.282 | 0.9045 | 0.903 | 0.903 | 0.989 | 0.886 | 0.819 | 0.7556 | 0.9743 |
| SSE | 3.832e-05 | 3.832e-05 | 3.844e-02 | 9.622e-04 | 2.246e-02 | 7.398e-02 | 2.064e-02 | |
| AIC | -42.2236 | -42.2236 | -14.5802 | -29.3303 | -16.7291 | -11.9609 | -17.0676 | |
| BIC | -43.451 | -43.451 | -15.8076 | -30.5577 | -17.9565 | -13.1883 | -18.295 |
| Experimental Mvttimes | Utility Grs | Utility Net | Utility Torque | Net Rwd Grs | Efficiency | Gross Cost | Net Cost | |
|---|---|---|---|---|---|---|---|---|
| alpha | 54.463 | 79.409 | 1.311 | |||||
| 2.506 | 0.8457 | 0.785 | 0.785 | 0.617 | 0.804 | 0.723 | 0.6627 | 0.8561 |
| 3.959 | 0.9018 | 0.84 | 0.84 | 0.777 | 0.84 | 0.768 | 0.7074 | 0.913 |
| 4.894 | 0.9262 | 0.868 | 0.868 | 0.867 | 0.86 | 0.79 | 0.7291 | 0.9407 |
| 6.282 | 0.9733 | 0.903 | 0.903 | 0.989 | 0.886 | 0.819 | 0.7556 | 0.9743 |
| SSE | 1.584e-02 | 1.584e-02 | 7.163e-02 | 1.757e-02 | 7.532e-02 | 1.575e-01 | 4.426e-04 | |
| AIC | -18.1272 | -18.1272 | -12.0902 | -17.7124 | -11.8891 | -8.9376 | -32.4363 | |
| BIC | -19.3546 | -19.3546 | -13.3177 | -18.9398 | -13.1165 | -10.165 | -33.6637 |
| Experimental Mvttimes | Utility Grs | Utility Net | Utility Torque | Net Rwd Grs | Efficiency | Gross Cost | Net Cost | |
|---|---|---|---|---|---|---|---|---|
| alpha | 54.463 | 79.409 | 1.311 | |||||
| 2.506 | 0.6673 | 0.785 | 0.785 | 0.617 | 0.804 | 0.723 | 0.6627 | 0.8561 |
| 3.959 | 0.7429 | 0.84 | 0.84 | 0.777 | 0.84 | 0.768 | 0.7074 | 0.913 |
| 4.894 | 0.7816 | 0.868 | 0.868 | 0.867 | 0.86 | 0.79 | 0.7291 | 0.9407 |
| 6.282 | 0.8234 | 0.903 | 0.903 | 0.989 | 0.886 | 0.819 | 0.7556 | 0.9743 |
| SSE | 3.709e-02 | 3.709e-02 | 3.842e-02 | 3.818e-02 | 3.822e-03 | 8.635e-03 | 1.127e-01 | |
| AIC | -14.7232 | -14.7232 | -14.5821 | -14.6066 | -23.8133 | -20.553 | -10.2786 | |
| BIC | -15.9506 | -15.9506 | -15.8095 | -15.834 | -25.0407 | -21.7804 | -11.506 |
| Experimental Mvttimes | Utility Grs | Utility Net | Utility Torque | Net Rwd Grs | Efficiency | Gross Cost | Net Cost | |
|---|---|---|---|---|---|---|---|---|
| alpha | 80.264 | 141.248 | 28.046 | |||||
| 2.506 | 0.7807 | 0.862 | 0.865 | 0.75 | 0.875 | 0.844 | 0.6627 | 0.8561 |
| 3.959 | 0.8441 | 0.904 | 0.904 | 0.803 | 0.905 | 0.881 | 0.7074 | 0.913 |
| 4.894 | 0.8677 | 0.927 | 0.925 | 0.838 | 0.922 | 0.901 | 0.7291 | 0.9407 |
| 6.282 | 0.9045 | 0.958 | 0.955 | 0.889 | 0.945 | 0.929 | 0.7556 | 0.9743 |
| SSE | 1.658e-02 | 1.654e-02 | 3.752e-03 | 1.720e-02 | 7.083e-03 | 7.398e-02 | 2.064e-02 | |
| AIC | -17.9424 | -17.9541 | -23.887 | -17.797 | -21.3454 | -11.9609 | -17.0676 | |
| BIC | -19.1698 | -19.1815 | -25.1144 | -19.0244 | -22.5728 | -13.1883 | -18.295 |
| Experimental Mvttimes | Utility Grs | Utility Net | Utility Torque | Net Rwd Grs | Efficiency | Gross Cost | Net Cost | |
|---|---|---|---|---|---|---|---|---|
| alpha | 80.264 | 141.248 | 28.046 | |||||
| 2.506 | 0.8457 | 0.862 | 0.865 | 0.75 | 0.875 | 0.844 | 0.6627 | 0.8561 |
| 3.959 | 0.9018 | 0.904 | 0.904 | 0.803 | 0.905 | 0.881 | 0.7074 | 0.913 |
| 4.894 | 0.9262 | 0.927 | 0.925 | 0.838 | 0.922 | 0.901 | 0.7291 | 0.9407 |
| 6.282 | 0.9733 | 0.958 | 0.955 | 0.889 | 0.945 | 0.929 | 0.7556 | 0.9743 |
| SSE | 5.057e-04 | 7.144e-04 | 3.381e-02 | 1.688e-03 | 3.035e-03 | 1.575e-01 | 4.426e-04 | |
| AIC | -31.9033 | -30.5216 | -15.0932 | -27.0808 | -24.7355 | -8.9376 | -32.4363 | |
| BIC | -33.1307 | -31.749 | -16.3206 | -28.3083 | -25.9629 | -10.165 | -33.6637 |
| Experimental Mvttimes | Utility Grs | Utility Net | Utility Torque | Net Rwd Grs | Efficiency | Gross Cost | Net Cost | |
|---|---|---|---|---|---|---|---|---|
| alpha | 80.264 | 141.248 | 28.046 | |||||
| 2.506 | 0.6673 | 0.862 | 0.865 | 0.75 | 0.875 | 0.844 | 0.6627 | 0.8561 |
| 3.959 | 0.7429 | 0.904 | 0.904 | 0.803 | 0.905 | 0.881 | 0.7074 | 0.913 |
| 4.894 | 0.7816 | 0.927 | 0.925 | 0.838 | 0.922 | 0.901 | 0.7291 | 0.9407 |
| 6.282 | 0.8234 | 0.958 | 0.955 | 0.889 | 0.945 | 0.929 | 0.7556 | 0.9743 |
| SSE | 1.031e-01 | 1.029e-01 | 1.794e-02 | 1.039e-01 | 7.571e-02 | 8.635e-03 | 1.127e-01 | |
| AIC | -10.6324 | -10.6401 | -17.6285 | -10.6017 | -11.8687 | -20.553 | -10.2786 | |
| BIC | -11.8598 | -11.8675 | -18.8559 | -11.8291 | -13.0961 | -21.7804 | -11.506 |
| Experimental Mvttimes | Utility Grs | Utility Net | Utility Torque | Net Rwd Grs | Efficiency | Gross Cost | Net Cost | |
|---|---|---|---|---|---|---|---|---|
| alpha | 75.113 | 94.012 | 25.188 | |||||
| 2.506 | 0.7807 | 0.691 | 0.692 | 0.529 | 0.663 | 0.663 | 0.6627 | 0.8561 |
| 3.959 | 0.8441 | 0.746 | 0.748 | 0.694 | 0.707 | 0.707 | 0.7074 | 0.913 |
| 4.894 | 0.8677 | 0.773 | 0.776 | 0.785 | 0.729 | 0.729 | 0.7291 | 0.9407 |
| 6.282 | 0.9045 | 0.807 | 0.811 | 0.927 | 0.756 | 0.756 | 0.7556 | 0.9743 |
| SSE | 3.613e-02 | 3.424e-02 | 9.322e-02 | 7.393e-02 | 7.393e-02 | 7.398e-02 | 2.064e-02 | |
| AIC | -14.8272 | -15.0421 | -11.0366 | -11.9639 | -11.9639 | -11.9609 | -17.0676 | |
| BIC | -16.0546 | -16.2695 | -12.264 | -13.1913 | -13.1913 | -13.1883 | -18.295 |
| Experimental Mvttimes | Utility Grs | Utility Net | Utility Torque | Net Rwd Grs | Efficiency | Gross Cost | Net Cost | |
|---|---|---|---|---|---|---|---|---|
| alpha | 75.113 | 94.012 | 25.188 | |||||
| 2.506 | 0.8457 | 0.691 | 0.692 | 0.529 | 0.663 | 0.663 | 0.6627 | 0.8561 |
| 3.959 | 0.9018 | 0.746 | 0.748 | 0.694 | 0.707 | 0.707 | 0.7074 | 0.913 |
| 4.894 | 0.9262 | 0.773 | 0.776 | 0.785 | 0.729 | 0.729 | 0.7291 | 0.9407 |
| 6.282 | 0.9733 | 0.807 | 0.811 | 0.927 | 0.756 | 0.756 | 0.7556 | 0.9743 |
| SSE | 9.934e-02 | 9.619e-02 | 1.656e-01 | 1.574e-01 | 1.574e-01 | 1.575e-01 | 4.426e-04 | |
| AIC | -10.7821 | -10.9111 | -8.7388 | -8.94 | -8.94 | -8.9376 | -32.4363 | |
| BIC | -12.0095 | -12.1385 | -9.9662 | -10.1674 | -10.1674 | -10.165 | -33.6637 |
| Experimental Mvttimes | Utility Grs | Utility Net | Utility Torque | Net Rwd Grs | Efficiency | Gross Cost | Net Cost | |
|---|---|---|---|---|---|---|---|---|
| alpha | 75.113 | 94.012 | 25.188 | |||||
| 2.506 | 0.6673 | 0.691 | 0.692 | 0.529 | 0.663 | 0.663 | 0.6627 | 0.8561 |
| 3.959 | 0.7429 | 0.746 | 0.748 | 0.694 | 0.707 | 0.707 | 0.7074 | 0.913 |
| 4.894 | 0.7816 | 0.773 | 0.776 | 0.785 | 0.729 | 0.729 | 0.7291 | 0.9407 |
| 6.282 | 0.8234 | 0.807 | 0.811 | 0.927 | 0.756 | 0.756 | 0.7556 | 0.9743 |
| SSE | 9.131e-04 | 8.203e-04 | 3.227e-02 | 8.613e-03 | 8.613e-03 | 8.635e-03 | 1.127e-01 | |
| AIC | -29.5398 | -29.9686 | -15.2799 | -20.5631 | -20.5631 | -20.553 | -10.2786 | |
| BIC | -30.7672 | -31.196 | -16.5074 | -21.7905 | -21.7905 | -21.7804 | -11.506 |
The utility combined alpha is using the alpha value predicted off fitting a utility model to the preferred and small target experiement at the same time. This alpha value is used to make figure ??.
This table shows the SSE for the 2a movement duration and peak velocity predictions.
| Model | Movement Duration SSE | Movement Duration AIC | Movement Duration BIC | Peak Velocity SSE | Peak Velocity AIC | Peak Velocity BIC | |
|---|---|---|---|---|---|---|---|
| SSE.2 | Accuracy Prob | 2.164e-03 | -2.81e+01 | -2.87e+01 | 1.130e-03 | -3.07e+01 | -3.13e+01 |
| SSE.3 | Met Cost Gross | 7.398e-02 | -1.40e+01 | -1.46e+01 | 4.167e-03 | -2.55e+01 | -2.61e+01 |
| SSE.4 | Met Cost Net | 2.064e-02 | -1.91e+01 | -1.97e+01 | 3.337e-03 | -2.64e+01 | -2.70e+01 |
| SSE.5 | Torque^2 | 3.844e-02 | -1.66e+01 | -1.72e+01 | 2.439e-03 | -2.76e+01 | -2.82e+01 |
| SSE.7 | Utility Gross | 3.832e-05 | -4.22e+01 | -4.35e+01 | 6.140e-04 | -3.11e+01 | -3.24e+01 |
| SSE.9 | Utility Net | 3.832e-05 | -4.22e+01 | -4.35e+01 | 6.140e-04 | -3.11e+01 | -3.24e+01 |
| SSE.10 | Utility Gross Combined Alpha | 6.750e-04 | -3.07e+01 | -3.20e+01 | 3.872e-04 | -3.30e+01 | -3.42e+01 |
| SSE.11 | Utility Net Combined Alpha | 2.433e-03 | -2.56e+01 | -2.68e+01 | 2.514e-04 | -3.47e+01 | -3.59e+01 |
| Model | Movement Duration SSE | Movement Duration AIC | Movement Duration BIC | Peak Velocity SSE | Peak Velocity AIC | Peak Velocity BIC | |
|---|---|---|---|---|---|---|---|
| SSE.2 | Accuracy Prob | 1.386e-02 | -2.07e+01 | -2.13e+01 | 3.207e-02 | -1.73e+01 | -1.79e+01 |
| SSE.3 | Met Cost Gross | 6.631e-04 | -3.28e+01 | -3.34e+01 | 1.014e-02 | -2.19e+01 | -2.25e+01 |
| SSE.4 | Met Cost Net | 7.998e-04 | -3.21e+01 | -3.27e+01 | 1.056e-02 | -2.17e+01 | -2.24e+01 |
| SSE.5 | Torque^2 | 3.154e-01 | -8.16e+00 | -8.77e+00 | 6.310e-02 | -1.46e+01 | -1.52e+01 |
| SSE.7 | Utility Gross | 2.279e-04 | -3.51e+01 | -3.63e+01 | 8.426e-03 | -2.07e+01 | -2.19e+01 |
| SSE.9 | Utility Net | 2.279e-04 | -3.51e+01 | -3.63e+01 | 8.426e-03 | -2.07e+01 | -2.19e+01 |
| SSE.10 | Utility Gross Combined Alpha | 2.558e-04 | -3.46e+01 | -3.59e+01 | 8.582e-03 | -2.06e+01 | -2.18e+01 |
| SSE.11 | Utility Net Combined Alpha | 3.548e-04 | -3.33e+01 | -3.45e+01 | 9.014e-03 | -2.04e+01 | -2.16e+01 |
Figure 9.1: Modeling Results
The utility combined alpha is using the alpha value predicted off fitting a utility model to the preferred and small target experiement at the same time. This alpha value is used to make figure ??.
This table shows the SSE for the 2b movement duration and peak velocity predictions.
| Model | Movement Duration SSE | Movement Duration AIC | Movement Duration BIC | Peak Velocity SSE | Peak Velocity AIC | Peak Velocity BIC | |
|---|---|---|---|---|---|---|---|
| SSE.2 | Accuracy Prob | 1.753e-02 | -1.97e+01 | -2.03e+01 | 1.510e-03 | -2.95e+01 | -3.01e+01 |
| SSE.3 | Met Cost Gross | 1.575e-01 | -1.09e+01 | -1.16e+01 | 1.411e-02 | -2.06e+01 | -2.12e+01 |
| SSE.4 | Met Cost Net | 4.426e-04 | -3.44e+01 | -3.51e+01 | 1.442e-04 | -3.89e+01 | -3.95e+01 |
| SSE.5 | Torque^2 | 7.163e-02 | -1.41e+01 | -1.47e+01 | 7.450e-03 | -2.31e+01 | -2.38e+01 |
| SSE.7 | Utility Gross | 5.057e-04 | -3.19e+01 | -3.31e+01 | 2.504e-04 | -3.47e+01 | -3.59e+01 |
| SSE.9 | Utility Net | 7.144e-04 | -3.05e+01 | -3.17e+01 | 2.837e-04 | -3.42e+01 | -3.54e+01 |
| SSE.10 | Utility Gross Combined Alpha | 2.260e-02 | -1.67e+01 | -1.79e+01 | 1.776e-03 | -2.69e+01 | -2.81e+01 |
| SSE.11 | Utility Net Combined Alpha | 3.024e-02 | -1.55e+01 | -1.68e+01 | 2.342e-03 | -2.58e+01 | -2.70e+01 |
| Model | Movement Duration SSE | Movement Duration AIC | Movement Duration BIC | Peak Velocity SSE | Peak Velocity AIC | Peak Velocity BIC | |
|---|---|---|---|---|---|---|---|
| SSE.2 | Accuracy Prob | 9.491e-03 | -2.22e+01 | -2.28e+01 | 2.533e-02 | -1.82e+01 | -1.89e+01 |
| SSE.3 | Met Cost Gross | 1.424e-04 | -3.90e+01 | -3.96e+01 | 6.723e-03 | -2.36e+01 | -2.42e+01 |
| SSE.4 | Met Cost Net | 1.762e-04 | -3.81e+01 | -3.87e+01 | 7.060e-03 | -2.34e+01 | -2.40e+01 |
| SSE.5 | Torque^2 | 3.376e-01 | -7.89e+00 | -8.50e+00 | 7.378e-02 | -1.40e+01 | -1.46e+01 |
| SSE.7 | Utility Gross | 2.272e-03 | -2.59e+01 | -2.71e+01 | 1.346e-02 | -1.88e+01 | -2.00e+01 |
| SSE.9 | Utility Net | 3.323e-03 | -2.44e+01 | -2.56e+01 | 1.550e-02 | -1.82e+01 | -1.94e+01 |
| SSE.10 | Utility Gross Combined Alpha | 1.001e-04 | -3.84e+01 | -3.96e+01 | 5.406e-03 | -2.24e+01 | -2.37e+01 |
| SSE.11 | Utility Net Combined Alpha | 7.777e-05 | -3.94e+01 | -4.06e+01 | 5.738e-03 | -2.22e+01 | -2.34e+01 |
Figure 10.1: Modeling Results
The utility combined alpha is using the alpha value predicted off fitting a utility model to the preferred and small target experiment at the same time. This alpha value is used to make figure ??.
This table shows the SSE for the 2b movement duration and peak velocity predictions.
| Model | Movement Duration SSE | Movement Duration AIC | Movement Duration BIC | Peak Velocity SSE | Peak Velocity AIC | Peak Velocity BIC | |
|---|---|---|---|---|---|---|---|
| SSE.2 | Accuracy Prob | 4.208e-02 | -1.62e+01 | -1.68e+01 | 6.517e-02 | -1.45e+01 | -1.51e+01 |
| SSE.3 | Met Cost Gross | 8.635e-03 | -2.26e+01 | -2.32e+01 | 2.855e-02 | -1.78e+01 | -1.84e+01 |
| SSE.4 | Met Cost Net | 1.127e-01 | -1.23e+01 | -1.29e+01 | 8.239e-02 | -1.35e+01 | -1.41e+01 |
| SSE.5 | Torque^2 | 3.842e-02 | -1.66e+01 | -1.72e+01 | 4.795e-02 | -1.57e+01 | -1.63e+01 |
| SSE.7 | Utility Gross | 9.131e-04 | -2.95e+01 | -3.08e+01 | 3.840e-02 | -1.46e+01 | -1.58e+01 |
| SSE.9 | Utility Net | 8.203e-04 | -3.00e+01 | -3.12e+01 | 3.898e-02 | -1.45e+01 | -1.58e+01 |
| SSE.10 | Utility Gross Combined Alpha | 2.845e-02 | -1.58e+01 | -1.70e+01 | 6.036e-02 | -1.28e+01 | -1.40e+01 |
| SSE.11 | Utility Net Combined Alpha | 2.134e-02 | -1.69e+01 | -1.82e+01 | 5.730e-02 | -1.30e+01 | -1.42e+01 |
| Model | Movement Duration SSE | Movement Duration AIC | Movement Duration BIC | Peak Velocity SSE | Peak Velocity AIC | Peak Velocity BIC | |
|---|---|---|---|---|---|---|---|
| SSE.2 | Accuracy Prob | 4.774e-02 | -1.57e+01 | -1.63e+01 | 3.463e-02 | -1.70e+01 | -1.76e+01 |
| SSE.3 | Met Cost Gross | 1.595e-02 | -2.01e+01 | -2.07e+01 | 1.165e-02 | -2.14e+01 | -2.20e+01 |
| SSE.4 | Met Cost Net | 1.661e-02 | -1.99e+01 | -2.06e+01 | 1.210e-02 | -2.12e+01 | -2.18e+01 |
| SSE.5 | Torque^2 | 2.123e-01 | -9.75e+00 | -1.04e+01 | 5.985e-02 | -1.48e+01 | -1.54e+01 |
| SSE.7 | Utility Gross | 8.253e-03 | -2.07e+01 | -2.20e+01 | 6.489e-03 | -2.17e+01 | -2.29e+01 |
| SSE.9 | Utility Net | 7.363e-03 | -2.12e+01 | -2.24e+01 | 5.906e-03 | -2.21e+01 | -2.33e+01 |
| SSE.10 | Utility Gross Combined Alpha | 1.338e-02 | -1.88e+01 | -2.00e+01 | 9.972e-03 | -2.00e+01 | -2.12e+01 |
| SSE.11 | Utility Net Combined Alpha | 1.404e-02 | -1.86e+01 | -1.98e+01 | 1.044e-02 | -1.98e+01 | -2.10e+01 |
Figure 11.1: Modeling Results